Transient analysis of energy equation of dynamical systems

Vibet, C.

doi:10.1109/13.779902

Cited by 10 publications

(3 citation statements)

References 3 publications

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“…In the case of the Dirac impulse command ⌫ ϭ ⌫ 0 ␦(t), the above technique can be applied, too, but new relationships have to be derived to redesign the graph. In particular, as the energy derivation can be added to the scheme given in Figure 2, proof of the effectiveness of the method can be obtained since the starting value of energy can be exactly computed from an analytic Lagrangian expression [15]. Finally, when a code with analog features is also used to solve Equation (11), the phase plane and/or acceleration plane or state space analysis allows numerical checking of the initial conditions.…”

Section: Nonlinear Systemsmentioning

confidence: 99%

Starting the codes that solve ordinary differential equations

Vibet

1999

Comput. Appl. Eng. Educ.

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This article presents a method to compute the initial conditions which are induced by smooth or jump commands into the processes modeled by nonlinear differential equations. The knowledge of such starting states is usually needed before running numerical programs that solve initial value problems on digital computers. The proposed technique, which is based on an extension of a graph method, permits the transient analysis of nonlinear systems just at the instant t = 0+. For the purpose of illustration, a mechanical process is analyzed on an standard PC platform. © 1999 John Wiley & Sons, Inc. Comput Appl Eng Educ 7: 196–202, 1999

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Section: Nonlinear Systemsmentioning

confidence: 99%

Starting the codes that solve ordinary differential equations

Vibet

1999

Comput. Appl. Eng. Educ.

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“…Complications in the use of the product rule for derivatives in one variable were considered in [3] when analysing the formula [14] (4.16)…”

Section: Bowen's Formulamentioning

confidence: 99%

Applications of the Thick Distributional Calculus

Yang,

Estrada

2014

Preprint

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We give several applications of the thick distributional calculus. We consider homogeneous thick distributions, point source fields, and higher order derivatives of order 0.1991 Mathematics Subject Classification. 46F10. Key words and phrases. Thick points, delta functions, distributions, generalized functions. * ,a (R n ) that vanish in R n \ K.1 Following the notation introduced by the late Professor Farassat [8], we shall denote distributional derivatives with an overbar.

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“…Thick distributions were introduced in one variable in [12] and in several variables in [36,37,38,39]. Thick distributions have found applications in understanding problems in several areas, such as quantum field theory [5], engineering [26,34], the understanding of singularities in mathematical physics as considered in [4] or in [6], or in obtaining formulas for the regularization of multipoles [8,25] that play a fundamental role in the ideas of the late professor Stora on convergent Feyman amplitudes [24,33]. They also appear in other problems, as generalizations of Frahm formulas [16] involving discontinuous test functions [17,37].…”

Section: Introductionmentioning

confidence: 99%

The Fourier transform of thick distributions

2020

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We first construct a space [Formula: see text] whose elements are test functions defined in [Formula: see text] the one point compactification of [Formula: see text] that have a thick expansion at infinity of special logarithmic type, and its dual space [Formula: see text] the space of sl-thick distributions. We show that there is a canonical projection of [Formula: see text] onto [Formula: see text] We study several sl-thick distributions and consider operations in [Formula: see text] We define and study the Fourier transform of thick test functions of [Formula: see text] and thick tempered distributions of [Formula: see text] We construct isomorphisms [Formula: see text] [Formula: see text] that extend the Fourier transform of tempered distributions, namely, [Formula: see text] and [Formula: see text] where [Formula: see text] are the canonical projections of [Formula: see text] or [Formula: see text] onto [Formula: see text] We determine the Fourier transform of several finite part regularizations and of general thick delta functions.

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Transient analysis of energy equation of dynamical systems

Cited by 10 publications

References 3 publications

Starting the codes that solve ordinary differential equations

Starting the codes that solve ordinary differential equations

Applications of the Thick Distributional Calculus

The Fourier transform of thick distributions

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